**Introduction to online Pythagorean identities tutor:**

** **Onlinemath tutoring is nothing but the technique of teaching through Internetwhere the students can learn math from the comfort from their home itself. The person who teach education to the students is said to be tutor. To demonstrate the trigonometric identities apply Pythagorean Theorem in terms of trigonometric functions is said to be Pythagorean trigonometric identity. In this section we shall discuss the Pythagoreanidentities through online tutor.

Pythagorean Identities follows the Pythagorean Theorem that can be stated as follows:

In a right angle triangle, sum of the squares of the opposite and adjacent sides is equal to the square of the hypotenuse.

The three Pythagorean identities are `c^2 = a^2+b^2`

Sin^{2}`theta` + Cos^{2}`theta` = 1

Sec^{2}`theta` - tan^{2}`theta` = 1

Csc^{2}`theta` - Cot^{2}`theta` = 1

We get the above Pythagorean Identities from the Pythagorean Theorem.

**Proof 1: **

Prove that sin^{2} A + cos^{2} A = 1.

**Solution:**

To prove sin^{2} A + cos^{2} A = 1.

Let us take a right angle triangle ABC to prove this.

From the figure ,

sin A = opp /hyp = AB / AC

cos A = adj / hyp = BC / AC.

Now,

sin^{2}A + cos^{2}A = (AB^{2} / AC^{2}) + (BC^{2} / AC^{2})

= (AB^{2} + BC^{2}) / AC^{2}

= AC^{2} /AC^{2} [Using Pythagorean Theorem]

=1

Hence we proved that, **sin ^{2}A + cos^{2}A = 1.**

**Proof 2: **

Prove that, tan^{2}A + 1 = sec^{2}A.

**Solution:**

We know that, sin^{2}A + cos^{2}A = 1--------- (1)

Dividing the equation (1) by cos^{2}A we get:

(sin^{2}A + cos^{2}A) / cos^{2}A = 1 / cos^{2}A

sin^{2}A / cos^{2}A + cos^{2}A / cos^{2}A = 1 / cos^{2}A

** **tan^{2}A + 1 = sec^{2}A

Hence proved that, tan^{2}A + 1 = sec^{2}A.

**Proof 3: **

Prove that, 1 + cot^{2}A = csc^{2}A

Solution:

We know that, sin^{2}A + cos^{2}A = 1--------- (1)

Dividing the equation (1) by sin^{2}A we get,

(sin^{2}A + cos^{2}A) / sin^{2}A = 1 / sin^{2}A

(sin^{2}A / sin^{2}A) + (cos^{2}A / sin^{2}A) = 1 / sin^{2}A

1 + cot^{2}A = csc^{2}A

Hence proved that, 1 + cot^{2}A = csc^{2}A